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Question

A basketball player is balancing a spinning basketball on the tip of his finger. The angular velocity of the ball slows down from 18.5 to 14.1 rad/s. During the slow-down, the angular displacement is 85.1 rad. Determine the time it takes for the ball to slow down.

Solution

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Answered 2 years ago
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Approach:

We are given initial velocity of the ball (ω1)(\omega_1),final velocity after slow-down (ω2)(\omega_2) and angular displacement (θ)(\theta). To find the time it takes for the ball to slow down, we will use equation of rotational kinematics:

θ=12(ω+ω0)t\begin{aligned} \theta&=\dfrac{1}{2} ( \omega+ \omega_0 )t \end{aligned}

where ω\omega is final angular velocity, in our case equal to ω1\omega_1, ω0\omega_0 is initial angular velocity, in our case equal to ω2\omega_2, and tt is time we are looking for.

Given values:

ω1=18.5 rads\omega_1=18.5 \ \tfrac{\text{rad}}{\text{s}}

ω2=14.1 rads\omega_2=14.1 \ \tfrac{\text{rad}}{\text{s}}

θ=85.1 rad\theta=85.1 \ \text{rad}

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